The Mu2e experiment at Fermilab will search for the Charged Lepton Flavour Violating (CLFV) process of neutrinoless conversion of muon to electron in the field of an Al nucleus. The experimental signature is a monochromatic 104.97 MeV conversion electron. One of the expected backgrounds to the conversion electron search is antiprotons produced by the proton beam at the Production Target and annihilating in the Stopping Target (ST). The background expected from antiprotons is low but highly uncertain due to the uncertainty in the antiproton production cross section for the Mu2e beam energy in the relevant angular region. Antiprotons are significantly slower than the other beam particles, so they cannot be efficiently suppressed by the time window cut used to reduce the prompt background. At Mu2e energies, antiproton annihilation at rest in the ST is the only source of events with multiple, simultaneous particle trajectories. We utilized this unique feature and developed a novel way to reconstruct the multi-track events and estimate the antiproton background in situ.